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<div class="title">test_casadi.cpp</div>  </div>
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<a href="../../dc/dd7/test__casadi_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#include &quot;gmock/gmock.h&quot;</span></div><div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor">#include &quot;gtest/gtest.h&quot;</span></div><div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;</div><div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#include &lt;casadi/casadi.hpp&gt;</span></div><div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="preprocessor">#include &lt;ctime&gt;</span></div><div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#include &lt;fstream&gt;</span></div><div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="preprocessor">#include &lt;iostream&gt;</span></div><div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;</div><div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="../../d0/d52/_dynamics_simulator_8h.html">Dynamics/DynamicsSimulator.h</a>&quot;</span></div><div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="../../d5/d9a/_floating_base_model_8h.html">Dynamics/FloatingBaseModel.h</a>&quot;</span></div><div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="../../d8/db6/_mini_cheetah_8h.html">Dynamics/MiniCheetah.h</a>&quot;</span></div><div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="../../d3/dc7/_quadruped_8h.html">Dynamics/Quadruped.h</a>&quot;</span></div><div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &lt;<a class="code" href="../../d3/d68/_utilities__print_8h.html">Utilities/Utilities_print.h</a>&gt;</span></div><div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;</div><div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;</div><div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">using namespace </span><a class="code" href="../../d7/d23/namespacecasadi.html">casadi</a>;</div><div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="keyword">using namespace </span><a class="code" href="../../d8/dcc/namespacestd.html">std</a>;</div><div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;</div><div class="line"><a name="l00019"></a><span class="lineno"><a class="line" href="../../dc/dd7/test__casadi_8cpp.html#ae22a77a911d57b6e51df80a32a050b94">   19</a></span>&#160;<a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae22a77a911d57b6e51df80a32a050b94">TEST</a>(<a class="code" href="../../d7/d23/namespacecasadi.html">casadi</a>, rocket_ipopt) {</div><div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;  cout &lt;&lt; <span class="stringliteral">&quot;program started&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;</div><div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;  <span class="comment">// Dimensions</span></div><div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;  <span class="keywordtype">int</span> nu = 20;   <span class="comment">// Number of control segments</span></div><div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;  <span class="keywordtype">int</span> nj = 100;  <span class="comment">// Number of integration steps per control segment</span></div><div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;</div><div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;  <span class="comment">// optimization variable</span></div><div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;  SX u = SX::sym(<span class="stringliteral">&quot;u&quot;</span>, nu);  <span class="comment">// control</span></div><div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;</div><div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;  SX s_0 = 0;  <span class="comment">// initial position</span></div><div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;  SX v_0 = 0;  <span class="comment">// initial speed</span></div><div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;  SX m_0 = 1;  <span class="comment">// initial mass</span></div><div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;</div><div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;  SX dt = 10.0 / (nj * nu);  <span class="comment">// time step</span></div><div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;  SX alpha = 0.05;           <span class="comment">// friction</span></div><div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;  SX beta = 0.1;             <span class="comment">// fuel consumption rate</span></div><div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;</div><div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;  <span class="comment">// Trajectory</span></div><div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;  vector&lt;SX&gt; s_k, v_k, m_k;</div><div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;</div><div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;  <span class="comment">// Integrate over the interval with Euler forward</span></div><div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;  SX s = s_0, v = v_0, m = m_0;</div><div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; nu; ++k) {</div><div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; nj; ++j) {</div><div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;      s += dt * v;</div><div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;      v += dt / m * (u(k) - alpha * v * v);</div><div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;      m += -dt * beta * u(k) * u(k);</div><div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;    }</div><div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    s_k.push_back(s);</div><div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;    v_k.push_back(v);</div><div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;    m_k.push_back(m);</div><div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;  }</div><div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;  SX s_all = vertcat(s_k), v_all = vertcat(v_k), m_all = vertcat(m_k);</div><div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;</div><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;  <span class="comment">// Objective function</span></div><div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;  SX <a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a> = dot(u, u);</div><div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;</div><div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;  <span class="comment">// Terminal constraints</span></div><div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;  SX g = vertcat(s, v, v_all);</div><div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;</div><div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;  <span class="comment">// Create the NLP</span></div><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  SXDict nlp = {{<span class="stringliteral">&quot;x&quot;</span>, u}, {<span class="stringliteral">&quot;f&quot;</span>, f}, {<span class="stringliteral">&quot;g&quot;</span>, g}};</div><div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;</div><div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;  <span class="comment">// Allocate an NLP solver and buffers</span></div><div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  Function solver = nlpsol(<span class="stringliteral">&quot;solver&quot;</span>, <span class="stringliteral">&quot;ipopt&quot;</span>, nlp);</div><div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;</div><div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;  <span class="comment">// Bounds on g</span></div><div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  vector&lt;double&gt; gmin = {10, 0};</div><div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;  vector&lt;double&gt; gmax = {10, 0};</div><div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;  gmin.resize(2 + nu, -numeric_limits&lt;double&gt;::infinity());</div><div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;  gmax.resize(2 + nu, 1.1);</div><div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;</div><div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;  <span class="comment">// Solve the problem</span></div><div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;  DMDict arg = {</div><div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;      {<span class="stringliteral">&quot;lbx&quot;</span>, -10}, {<span class="stringliteral">&quot;ubx&quot;</span>, 10}, {<span class="stringliteral">&quot;x0&quot;</span>, 0.4}, {<span class="stringliteral">&quot;lbg&quot;</span>, gmin}, {<span class="stringliteral">&quot;ubg&quot;</span>, gmax}};</div><div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;  DMDict res = solver(arg);</div><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;</div><div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;  <span class="comment">// Print the optimal cost</span></div><div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;  <span class="keywordtype">double</span> cost(res.at(<span class="stringliteral">&quot;f&quot;</span>));</div><div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;  cout &lt;&lt; <span class="stringliteral">&quot;optimal cost: &quot;</span> &lt;&lt; cost &lt;&lt; endl;</div><div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;</div><div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;  <span class="comment">// Print the optimal solution</span></div><div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  vector&lt;double&gt; uopt(res.at(<span class="stringliteral">&quot;x&quot;</span>));</div><div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  cout &lt;&lt; <span class="stringliteral">&quot;optimal control: &quot;</span> &lt;&lt; uopt &lt;&lt; endl;</div><div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;</div><div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;  <span class="comment">// Get the state trajectory</span></div><div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;  Function xfcn(<span class="stringliteral">&quot;xfcn&quot;</span>, {u}, {s_all, v_all, m_all});</div><div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;  vector&lt;double&gt; sopt, vopt, mopt;</div><div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;  xfcn({uopt}, {&amp;sopt, &amp;vopt, &amp;mopt});</div><div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;  cout &lt;&lt; <span class="stringliteral">&quot;position: &quot;</span> &lt;&lt; sopt &lt;&lt; endl;</div><div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;  cout &lt;&lt; <span class="stringliteral">&quot;velocity: &quot;</span> &lt;&lt; vopt &lt;&lt; endl;</div><div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;  cout &lt;&lt; <span class="stringliteral">&quot;mass:     &quot;</span> &lt;&lt; mopt &lt;&lt; endl;</div><div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;</div><div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;  <span class="keywordtype">bool</span> b_save_matlab_file(<span class="keyword">false</span>);</div><div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;  <span class="keywordflow">if</span> (b_save_matlab_file) {</div><div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    <span class="comment">// Create Matlab script to plot the solution</span></div><div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    ofstream file;</div><div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    <span class="keywordtype">string</span> filename = <span class="stringliteral">&quot;rocket_ipopt_results.m&quot;</span>;</div><div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;    file.open(filename.c_str());</div><div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;% Results file from &quot;</span> __FILE__ &lt;&lt; endl;</div><div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;% Generated &quot;</span> __DATE__ <span class="stringliteral">&quot; at &quot;</span> __TIME__ &lt;&lt; endl;</div><div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    file &lt;&lt; endl;</div><div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;cost = &quot;</span> &lt;&lt; cost &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;u = &quot;</span> &lt;&lt; uopt &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;</div><div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    <span class="comment">// Save results to file</span></div><div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;t = linspace(0,10.0,&quot;</span> &lt;&lt; nu &lt;&lt; <span class="stringliteral">&quot;);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;s = &quot;</span> &lt;&lt; sopt &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;v = &quot;</span> &lt;&lt; vopt &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;m = &quot;</span> &lt;&lt; mopt &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;</div><div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    <span class="comment">// Finalize the results file</span></div><div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    file &lt;&lt; endl;</div><div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;% Plot the results&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;figure(1);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;clf;&quot;</span> &lt;&lt; endl &lt;&lt; endl;</div><div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;</div><div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;subplot(2,2,1);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;plot(t,s);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;grid on;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;xlabel(&#39;time [s]&#39;);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;ylabel(&#39;position [m]&#39;);&quot;</span> &lt;&lt; endl &lt;&lt; endl;</div><div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;</div><div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;subplot(2,2,2);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;plot(t,v);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;grid on;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;xlabel(&#39;time [s]&#39;);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;ylabel(&#39;velocity [m/s]&#39;);&quot;</span> &lt;&lt; endl &lt;&lt; endl;</div><div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;</div><div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;subplot(2,2,3);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;plot(t,m);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;grid on;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;xlabel(&#39;time [s]&#39;);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;ylabel(&#39;mass [kg]&#39;);&quot;</span> &lt;&lt; endl &lt;&lt; endl;</div><div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;</div><div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;subplot(2,2,4);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;plot(t,u);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;grid on;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;xlabel(&#39;time [s]&#39;);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;ylabel(&#39;Thrust [kg m/s^2]&#39;);&quot;</span> &lt;&lt; endl &lt;&lt; endl;</div><div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;</div><div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;    file.close();</div><div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;    cout &lt;&lt; <span class="stringliteral">&quot;Results saved to \&quot;&quot;</span> &lt;&lt; filename &lt;&lt; <span class="stringliteral">&quot;\&quot;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;  }</div><div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;}</div><div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;</div><div class="line"><a name="l00146"></a><span class="lineno"><a class="line" href="../../dc/dd7/test__casadi_8cpp.html#a7513aad5ea59867b3800abeed95c25cd">  146</a></span>&#160;<a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae22a77a911d57b6e51df80a32a050b94">TEST</a>(<a class="code" href="../../d7/d23/namespacecasadi.html">casadi</a>, part1) {</div><div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;  <span class="comment">// Optimization variables</span></div><div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;  MX x = MX::sym(<span class="stringliteral">&quot;x&quot;</span>, 2);</div><div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;</div><div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;  <span class="comment">// Objective</span></div><div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;  MX <a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a> = x(0) * x(0) + x(1) * x(1);</div><div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;</div><div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;  <span class="comment">// Constraints</span></div><div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;  MX g = x(0) + x(1) - 10;</div><div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;</div><div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;  <span class="comment">// Create an NLP solver instance</span></div><div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;  Function solver = nlpsol(<span class="stringliteral">&quot;solver&quot;</span>, <span class="stringliteral">&quot;ipopt&quot;</span>, {{<span class="stringliteral">&quot;x&quot;</span>, x}, {<span class="stringliteral">&quot;f&quot;</span>, f}, {<span class="stringliteral">&quot;g&quot;</span>, g}});</div><div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;</div><div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;  <span class="comment">// Generate C code for the NLP functions</span></div><div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  solver.generate_dependencies(<span class="stringliteral">&quot;nlp.c&quot;</span>);</div><div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;</div><div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;  <span class="comment">// Just-in-time compilation?</span></div><div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;  <span class="keywordtype">bool</span> jit = <span class="keyword">false</span>;</div><div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;  <span class="keywordflow">if</span> (jit) {</div><div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;    <span class="comment">// Create a new NLP solver instance using just-in-time compilation</span></div><div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;    solver = nlpsol(<span class="stringliteral">&quot;solver&quot;</span>, <span class="stringliteral">&quot;ipopt&quot;</span>, <span class="stringliteral">&quot;nlp.c&quot;</span>);</div><div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    <span class="comment">// Compile the c-code</span></div><div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    <span class="keywordtype">int</span> flag = system(<span class="stringliteral">&quot;gcc -fPIC -shared -O3 nlp.c -o nlp.so&quot;</span>);</div><div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    casadi_assert(flag == 0, <span class="stringliteral">&quot;Compilation failed&quot;</span>);</div><div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;</div><div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    <span class="comment">// Create a new NLP solver instance from the compiled code</span></div><div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    solver = nlpsol(<span class="stringliteral">&quot;solver&quot;</span>, <span class="stringliteral">&quot;ipopt&quot;</span>, <span class="stringliteral">&quot;nlp.so&quot;</span>);</div><div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;  }</div><div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;</div><div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;  <span class="comment">// Bounds and initial guess</span></div><div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;  std::map&lt;std::string, DM&gt; arg, res;</div><div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  arg[<span class="stringliteral">&quot;lbx&quot;</span>] = -DM::inf();</div><div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;  arg[<span class="stringliteral">&quot;ubx&quot;</span>] = DM::inf();</div><div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;  arg[<span class="stringliteral">&quot;lbg&quot;</span>] = 0;</div><div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;  arg[<span class="stringliteral">&quot;ubg&quot;</span>] = DM::inf();</div><div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;  arg[<span class="stringliteral">&quot;x0&quot;</span>] = 0;</div><div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;</div><div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;  <span class="comment">// Solve the NLP</span></div><div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;  res = solver(arg);</div><div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;</div><div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;  <span class="comment">// Print solution</span></div><div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;  cout &lt;&lt; <span class="stringliteral">&quot;-----&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;  cout &lt;&lt; <span class="stringliteral">&quot;objective at solution = &quot;</span> &lt;&lt; res.at(<span class="stringliteral">&quot;f&quot;</span>) &lt;&lt; endl;</div><div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;  cout &lt;&lt; <span class="stringliteral">&quot;primal solution = &quot;</span> &lt;&lt; res.at(<span class="stringliteral">&quot;x&quot;</span>) &lt;&lt; endl;</div><div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;  cout &lt;&lt; <span class="stringliteral">&quot;dual solution (x) = &quot;</span> &lt;&lt; res.at(<span class="stringliteral">&quot;lam_x&quot;</span>) &lt;&lt; endl;</div><div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  cout &lt;&lt; <span class="stringliteral">&quot;dual solution (g) = &quot;</span> &lt;&lt; res.at(<span class="stringliteral">&quot;lam_g&quot;</span>) &lt;&lt; endl;</div><div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;}</div><div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;</div><div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;<span class="comment">// dx/dt = f(x,u)</span></div><div class="line"><a name="l00202"></a><span class="lineno"><a class="line" href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">  202</a></span>&#160;MX <a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a>(<span class="keyword">const</span> MX&amp; x, <span class="keyword">const</span> MX&amp; u) { <span class="keywordflow">return</span> vertcat(x(1), u - x(1)); }</div><div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;</div><div class="line"><a name="l00204"></a><span class="lineno"><a class="line" href="../../dc/dd7/test__casadi_8cpp.html#a497fae96e7467082b4fd05247a84511c">  204</a></span>&#160;<a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae22a77a911d57b6e51df80a32a050b94">TEST</a>(<a class="code" href="../../d7/d23/namespacecasadi.html">casadi</a>, race_car) {</div><div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;  <span class="comment">// Car race along a track</span></div><div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;  <span class="comment">// ----------------------</span></div><div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;  <span class="comment">// An optimal control problem (OCP),</span></div><div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;  <span class="comment">// solved with direct multiple-shooting.</span></div><div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;  <span class="comment">//</span></div><div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;  <span class="comment">// For more information see: http://labs.casadi.org/OCP</span></div><div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;</div><div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;  <span class="keywordtype">int</span> N = 100;  <span class="comment">// number of control intervals</span></div><div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;</div><div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;  <span class="keyword">auto</span> opti = casadi::Opti();  <span class="comment">// Optimization problem</span></div><div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;</div><div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;  Slice all;</div><div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;  <span class="comment">// ---- decision variables ---------</span></div><div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;  <span class="keyword">auto</span> <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a> = opti.variable(2, N + 1);  <span class="comment">// state trajectory</span></div><div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;  <span class="keyword">auto</span> pos = <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(0, all);</div><div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;  <span class="keyword">auto</span> speed = <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(1, all);</div><div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  <span class="keyword">auto</span> U = opti.variable(1, N);  <span class="comment">// control trajectory (throttle)</span></div><div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;  <span class="keyword">auto</span> T = opti.variable();      <span class="comment">// final time</span></div><div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;</div><div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;  <span class="comment">// ---- objective          ---------</span></div><div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;  opti.minimize(T);  <span class="comment">// race in minimal time</span></div><div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;</div><div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;  <span class="comment">// ---- dynamic constraints --------</span></div><div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;  <span class="keyword">auto</span> dt = T / N;</div><div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; N; ++k) {</div><div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    <span class="keyword">auto</span> k1 = <a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a>(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(all, k), U(all, k));</div><div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;    <span class="keyword">auto</span> k2 = <a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a>(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(all, k) + dt / 2 * k1, U(all, k));</div><div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;    <span class="keyword">auto</span> k3 = <a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a>(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(all, k) + dt / 2 * k2, U(all, k));</div><div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;    <span class="keyword">auto</span> k4 = <a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a>(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(all, k) + dt * k3, U(all, k));</div><div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;    <span class="keyword">auto</span> x_next = <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(all, k) + dt / 6 * (k1 + 2 * k2 + 2 * k3 + k4);</div><div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;    opti.subject_to(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(all, k + 1) == x_next);  <span class="comment">// close the gaps</span></div><div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;  }</div><div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;</div><div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;  <span class="comment">// ---- path constraints -----------</span></div><div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;  opti.subject_to(speed &lt;= 1 - sin(2 * pi * pos) / 2);  <span class="comment">// track speed limit</span></div><div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;  opti.subject_to(0 &lt;= U &lt;= 1);                         <span class="comment">// control is limited</span></div><div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;</div><div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;  <span class="comment">// ---- boundary conditions --------</span></div><div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;  opti.subject_to(pos(1) == 0);    <span class="comment">// start at position 0 ...</span></div><div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;  opti.subject_to(speed(1) == 0);  <span class="comment">// ... from stand-still</span></div><div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;  opti.subject_to(pos(N) == 1);    <span class="comment">// finish line at position 1</span></div><div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;</div><div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;  <span class="comment">// ---- misc. constraints  ----------</span></div><div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;  opti.subject_to(T &gt;= 0);  <span class="comment">// Time must be positive</span></div><div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;</div><div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;  <span class="comment">// ---- initial values for solver ---</span></div><div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;  opti.set_initial(speed, 1);</div><div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;  opti.set_initial(T, 1);</div><div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;</div><div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;  <span class="comment">// ---- solve NLP              ------</span></div><div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;  opti.solver(<span class="stringliteral">&quot;ipopt&quot;</span>);     <span class="comment">// set numerical backend</span></div><div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;  <span class="keyword">auto</span> sol = opti.solve();  <span class="comment">// actual solve</span></div><div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;</div><div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;  <span class="keywordtype">bool</span> b_matlab_file(<span class="keyword">false</span>);</div><div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;  <span class="keywordflow">if</span> (b_matlab_file) {</div><div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;    <span class="comment">// Create Matlab script to plot the solution</span></div><div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;    ofstream file;</div><div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;    <span class="keywordtype">string</span> filename = <span class="stringliteral">&quot;race_car_results.m&quot;</span>;</div><div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;    file.open(filename.c_str());</div><div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;% Results file from &quot;</span> __FILE__ &lt;&lt; endl;</div><div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;% Generated &quot;</span> __DATE__ <span class="stringliteral">&quot; at &quot;</span> __TIME__ &lt;&lt; endl;</div><div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;    file &lt;&lt; endl;</div><div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;</div><div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;    <span class="comment">// Save results to file</span></div><div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;t = linspace(0,&quot;</span> &lt;&lt; sol.value(T) &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; N &lt;&lt; <span class="stringliteral">&quot;+1);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;speed = &quot;</span> &lt;&lt; std::vector&lt;double&gt;(sol.value(speed)) &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;pos = &quot;</span> &lt;&lt; std::vector&lt;double&gt;(sol.value(pos)) &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;U = &quot;</span> &lt;&lt; std::vector&lt;double&gt;(sol.value(U)) &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;</div><div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;figure;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;hold on;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;plot(t,speed);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;plot(t,pos);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;plot(t,1-sin(2*pi*pos)/2,&#39;r--&#39;);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;stairs(t(1:end-1),U,&#39;k&#39;);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;xlabel(&#39;Time [s]&#39;);&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;legend(&#39;speed&#39;,&#39;pos&#39;,&#39;speed &quot;</span></div><div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;            <span class="stringliteral">&quot;limit&#39;,&#39;throttle&#39;,&#39;Location&#39;,&#39;northwest&#39;);&quot;</span></div><div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;         &lt;&lt; endl;</div><div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;</div><div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;    <span class="comment">// Have a look at the constraint Jacobian</span></div><div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;    jacobian(opti.g(), opti.x()).sparsity().spy_matlab(<span class="stringliteral">&quot;race_car_jac_g.m&quot;</span>);</div><div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;</div><div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;figure&quot;</span> &lt;&lt; std::endl;</div><div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;race_car_jac_g;&quot;</span> &lt;&lt; std::endl;</div><div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;xlabel(&#39;decision variables&#39;);&quot;</span> &lt;&lt; std::endl;</div><div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;ylabel(&#39;constraints&#39;);&quot;</span> &lt;&lt; std::endl;</div><div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;print(&#39;jac_sp&#39;,&#39;-dpng&#39;);&quot;</span> &lt;&lt; std::endl;</div><div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;  }</div><div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;}</div><div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;</div><div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;<span class="comment">// dx/dt = f(x,u)</span></div><div class="line"><a name="l00297"></a><span class="lineno"><a class="line" href="../../dc/dd7/test__casadi_8cpp.html#a37cd3654eae85ab1ac98486587c52e22">  297</a></span>&#160;MX <a class="code" href="../../dc/dd7/test__casadi_8cpp.html#a37cd3654eae85ab1ac98486587c52e22">simple_dyn</a>(<span class="keyword">const</span> MX&amp; x, <span class="keyword">const</span> MX&amp; u, <span class="keyword">const</span> MX&amp; P, <span class="keywordtype">int</span> i) { </div><div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;  <span class="keywordtype">double</span> I(0.21);</div><div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;  <span class="keywordtype">double</span> M(8.91);</div><div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;  <span class="keywordtype">double</span> g(9.81);</div><div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;</div><div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;  <span class="keywordflow">if</span>( i&lt;15 ){</div><div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;    <span class="keywordflow">return</span> vertcat (vertcat(x(3), x(4), x(5)), </div><div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;        vertcat(u(0)/M, u(1)/M -g), ((P(1) - x(1))*u(0) - (P(0) - x(0)) * u(1))/I );  <span class="comment">// Velocity</span></div><div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;  }<span class="keywordflow">else</span>{</div><div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;    <span class="keywordflow">return</span> vertcat (vertcat(x(3), x(4), x(5)), </div><div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;        vertcat(u(0)/M, u(1)/M -g), ((P(3) - x(1))*u(0) - (P(2) - x(0)) * u(1))/I );  <span class="comment">// Velocity</span></div><div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;  }</div><div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;}</div><div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;</div><div class="line"><a name="l00311"></a><span class="lineno"><a class="line" href="../../dc/dd7/test__casadi_8cpp.html#a5843f22963360bdd28a7a608a914b6ac">  311</a></span>&#160;<a class="code" href="../../d9/d8e/cpp_types_8h.html#ae2e5a0a178a2c528d8aa939f85db7a3e">DVec&lt;double&gt;</a> <a class="code" href="../../dc/dd7/test__casadi_8cpp.html#a5843f22963360bdd28a7a608a914b6ac">simple_dyn_vec</a>(<span class="keyword">const</span> <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae2e5a0a178a2c528d8aa939f85db7a3e">DVec&lt;double&gt;</a> &amp; x, </div><div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;    <span class="keyword">const</span> <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae2e5a0a178a2c528d8aa939f85db7a3e">DVec&lt;double&gt;</a>&amp; u, <span class="keyword">const</span> <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae2e5a0a178a2c528d8aa939f85db7a3e">DVec&lt;double&gt;</a>&amp; P, <span class="keywordtype">int</span> i) { </div><div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;  <span class="keywordtype">double</span> I(0.21);</div><div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;  <span class="keywordtype">double</span> M(8.91);</div><div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;  <span class="keywordtype">double</span> g(9.81);</div><div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;</div><div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae2e5a0a178a2c528d8aa939f85db7a3e">DVec&lt;double&gt;</a> ret(6);</div><div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;  <span class="keywordflow">if</span>( i&lt;15 ){</div><div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;    ret &lt;&lt; x(3), x(4), x(5), </div><div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;        u(0)/M, u(1)/M -g, ((P(1) - x(1))*u(0) - (P(0) - x(0)) * u(1))/I ;  <span class="comment">// Velocity</span></div><div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;  }<span class="keywordflow">else</span>{</div><div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;    ret &lt;&lt; x(3), x(4), x(5), </div><div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;        u(0)/M, u(1)/M -g, ((P(3) - x(1))*u(0) - (P(2) - x(0)) * u(1))/I ;  <span class="comment">// Velocity</span></div><div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;  }</div><div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;</div><div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;  <span class="keywordflow">return</span> ret;</div><div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;}</div><div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;</div><div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;<span class="comment">// [x, y, theta, dot_x, dot_y, dot_theta]</span></div><div class="line"><a name="l00330"></a><span class="lineno"><a class="line" href="../../dc/dd7/test__casadi_8cpp.html#a0401350aa7274070a3b1a8f9fdac345a">  330</a></span>&#160;<a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae22a77a911d57b6e51df80a32a050b94">TEST</a>(<a class="code" href="../../d7/d23/namespacecasadi.html">casadi</a>, jump_opt) {</div><div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;  <span class="comment">// Mass Matrix Test</span></div><div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;  <span class="comment">//FloatingBaseModel&lt;double&gt; cheetah = buildMiniCheetah&lt;double&gt;().buildModel();</span></div><div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;  <span class="comment">//FBModelState&lt;double&gt; state;</span></div><div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;  <span class="comment">//state.q = DVec&lt;double&gt;::Zero(cheetah::num_act_joint);</span></div><div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;  <span class="comment">//state.qd = DVec&lt;double&gt;::Zero(cheetah::num_act_joint);</span></div><div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160; </div><div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;  <span class="comment">//for(size_t i(0); i&lt;4; ++i){</span></div><div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;    <span class="comment">//state.q[1 + 3*i] = -M_PI/2.;</span></div><div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;    <span class="comment">//state.q[2 + 3*i] = M_PI;</span></div><div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;  <span class="comment">//}</span></div><div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;    <span class="comment">//state.q[7] = M_PI/2.;</span></div><div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;    <span class="comment">//state.q[10] = M_PI/2.;</span></div><div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;  <span class="comment">//state.bodyPosition.setZero();</span></div><div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;  <span class="comment">//state.bodyVelocity.setZero();</span></div><div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;  <span class="comment">//state.bodyOrientation[0] = 1.;</span></div><div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;  <span class="comment">//state.bodyOrientation[1] = 0.;</span></div><div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;  <span class="comment">//state.bodyOrientation[2] = 0.;</span></div><div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;  <span class="comment">//state.bodyOrientation[3] = 0.;</span></div><div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;</div><div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;  <span class="comment">//cheetah.setState(state);</span></div><div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;  <span class="comment">//cheetah.forwardKinematics();</span></div><div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;</div><div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;  <span class="comment">//DMat&lt;double&gt; A = cheetah.massMatrix();</span></div><div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;  <span class="comment">//std::cout&lt;&lt;A&lt;&lt;std::endl;</span></div><div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;  </div><div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;  <span class="comment">// Jump optimization</span></div><div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;  <span class="comment">// ----------------------</span></div><div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;  <span class="comment">// An optimal control problem (OCP),</span></div><div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;  <span class="comment">// solved with direct multiple-shooting.</span></div><div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;  <span class="comment">//</span></div><div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;  <span class="comment">// For more information see: http://labs.casadi.org/OCP</span></div><div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;</div><div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;  <span class="keywordtype">int</span> N = 31;  <span class="comment">// number of control intervals</span></div><div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;  <span class="keywordtype">int</span> N_fc = 15;</div><div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;  <span class="comment">//int N_air = 1;</span></div><div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;  <span class="comment">//int N_hc = 15;</span></div><div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;  <span class="keyword">auto</span> opti = casadi::Opti();  <span class="comment">// Optimization problem</span></div><div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;</div><div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;  Slice all;</div><div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;  <span class="comment">// ---- decision variables ---------</span></div><div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;  <span class="keyword">auto</span> <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a> = opti.variable(6, N+1);  <span class="comment">// state trajectory</span></div><div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;  <span class="keyword">auto</span> P = opti.variable(4);  <span class="comment">// Landing Location</span></div><div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;  <span class="keyword">auto</span> F = opti.variable(2, N);  <span class="comment">// Reaction force (15: front, 1: air, 15: hind)</span></div><div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;  <span class="keyword">auto</span> cost = opti.variable();</div><div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;</div><div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae2e5a0a178a2c528d8aa939f85db7a3e">DVec&lt;double&gt;</a> X0(6); X0.setZero();</div><div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;  X0&lt;&lt; 0.0, 0.2, 0.2, 0.5, -0.1, 0.1;</div><div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;</div><div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae2e5a0a178a2c528d8aa939f85db7a3e">DVec&lt;double&gt;</a> Xf(6); Xf.setZero();</div><div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;  <span class="comment">//Xf&lt;&lt; 0.1, 0.2, -M_PI/4., 0.1, 0.3, 0.0;</span></div><div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;  Xf&lt;&lt; 0.5, 0.23, -M_PI/4., 0.8, 0.8, 0.1;</div><div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;</div><div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;  cost = (<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(0,N) - Xf(0)) * (<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(0,N) - Xf(0))</div><div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;    + (<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(1,N) - Xf(1)) * (<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(1,N) - Xf(1))</div><div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;    + (<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(2,N) - Xf(2)) * (<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(2,N) - Xf(2))</div><div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;    + (<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(3,N) - Xf(3)) * (<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(3,N) - Xf(3))</div><div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;    + (<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(4,N) - Xf(4)) * (<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(4,N) - Xf(4))</div><div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;    + (<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(5,N) - Xf(5)) * (<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(5,N) - Xf(5));</div><div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;  <span class="comment">//</span></div><div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;  <span class="comment">// ---- objective          ---------</span></div><div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;  opti.minimize(cost);  <span class="comment">// race in minimal time</span></div><div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;</div><div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;  <span class="comment">// ---- dynamic constraints --------</span></div><div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;  <span class="keyword">auto</span> dt = 0.01;</div><div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;  <span class="keywordtype">double</span> mu(0.5);</div><div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;</div><div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; N; ++k) {</div><div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;    <span class="keyword">auto</span> dX = <a class="code" href="../../dc/dd7/test__casadi_8cpp.html#a37cd3654eae85ab1ac98486587c52e22">simple_dyn</a>(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(all, k), F(all, k), P, k);</div><div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;    <span class="keyword">auto</span> X_next = <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(all, k) + dt * dX;</div><div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;    opti.subject_to(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(all, k + 1) == X_next);  <span class="comment">// close the gaps</span></div><div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;</div><div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;    <span class="comment">// ---- contact constraints -----------</span></div><div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;    opti.subject_to(-mu * F(1,k) &lt;= F(0, k) &lt;= mu* F(1,k)); </div><div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;    opti.subject_to(0&lt;=F(1,k) &lt;= 300.); </div><div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;    <span class="comment">// Kinematics constraints</span></div><div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;    opti.subject_to (-0.15 &lt;= P(0) &lt;= 0.15);</div><div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;    opti.subject_to (-0.15 &lt;= P(2) &lt;= 0.15);</div><div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;    opti.subject_to (P(1) == 0.);</div><div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;    opti.subject_to (P(3) == 0.);</div><div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;</div><div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;  }</div><div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;  opti.subject_to(F(1, N_fc) == 0.);</div><div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;</div><div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i(0); i&lt;6; ++i){</div><div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;    opti.subject_to(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(i, 1) == X0(i)); </div><div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;  }</div><div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;  <span class="comment">// ---- solve NLP              ------</span></div><div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;  opti.solver(<span class="stringliteral">&quot;ipopt&quot;</span>);     <span class="comment">// set numerical backend</span></div><div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;  <span class="keyword">auto</span> sol = opti.solve();  <span class="comment">// actual solve</span></div><div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;  <span class="comment">//std::vector&lt;double&gt; result = std::vector&lt;double&gt;(sol.debug.value(X(0, all) ) );</span></div><div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;  </div><div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;  <span class="comment">//for(int i(0); i&lt;N; ++i){</span></div><div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;    <span class="comment">//printf(&quot;xb: %f\n&quot;, result[i]);</span></div><div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;  <span class="comment">//}</span></div><div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;</div><div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;</div><div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;</div><div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> k(0); k&lt;N; ++k){</div><div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;    std::vector&lt;double&gt; x_std_vec = std::vector&lt;double&gt;(sol.value(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(all, k)));</div><div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;    std::vector&lt;double&gt; x_next_std_vec = std::vector&lt;double&gt;(sol.value(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(all, k+1)));</div><div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;    std::vector&lt;double&gt; <a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a> = std::vector&lt;double&gt;(sol.value(F(all, k)));</div><div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;    std::vector&lt;double&gt; p = std::vector&lt;double&gt;(sol.value(P(all)));</div><div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;</div><div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;    <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae2e5a0a178a2c528d8aa939f85db7a3e">DVec&lt;double&gt;</a> x_current(6);</div><div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;    <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae2e5a0a178a2c528d8aa939f85db7a3e">DVec&lt;double&gt;</a> x_next(6);</div><div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;    <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae2e5a0a178a2c528d8aa939f85db7a3e">DVec&lt;double&gt;</a> f_eigen(2); </div><div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;    f_eigen[0] = f[0];</div><div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;    f_eigen[1] = f[1];</div><div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;</div><div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;    <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae2e5a0a178a2c528d8aa939f85db7a3e">DVec&lt;double&gt;</a> p_eigen(4); </div><div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;    p_eigen[0] = p[0]; </div><div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;    p_eigen[1] = p[1]; </div><div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;    p_eigen[2] = p[2]; </div><div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;    p_eigen[3] = p[3]; </div><div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;</div><div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i(0); i&lt;6; ++i){</div><div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;      x_current[i] = x_std_vec[i];</div><div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;      x_next[i] = x_next_std_vec[i];</div><div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;    }</div><div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;    <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae2e5a0a178a2c528d8aa939f85db7a3e">DVec&lt;double&gt;</a> dx_eigen = <a class="code" href="../../dc/dd7/test__casadi_8cpp.html#a5843f22963360bdd28a7a608a914b6ac">simple_dyn_vec</a>(x_current, f_eigen, p_eigen, k);</div><div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;    <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae2e5a0a178a2c528d8aa939f85db7a3e">DVec&lt;double&gt;</a> x_next_eigen = x_current + dt * dx_eigen;</div><div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;    EXPECT_TRUE(<a class="code" href="../../de/dda/_math_utilities_8h.html#aa06ec79f1e3170ea41b58ffbf35b9fb6">almostEqual</a>(x_next, x_next_eigen, .0001));</div><div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;    <a class="code" href="../../d3/d68/_utilities__print_8h.html#a0d5ac61bf2b7611715c750cf271b33e9">pretty_print</a>(x_next, std::cout, <span class="stringliteral">&quot;x_next_casadi&quot;</span>);</div><div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;    <a class="code" href="../../d3/d68/_utilities__print_8h.html#a0d5ac61bf2b7611715c750cf271b33e9">pretty_print</a>(x_next_eigen, std::cout, <span class="stringliteral">&quot;x_next_eigen&quot;</span>);</div><div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;    printf(<span class="stringliteral">&quot;\n&quot;</span>);</div><div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;  }</div><div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;</div><div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;  <span class="keywordtype">bool</span> b_matlab_file(<span class="keyword">true</span>);</div><div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;  <span class="keywordflow">if</span> (b_matlab_file) {</div><div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;    ofstream file;</div><div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;    <span class="keywordtype">string</span> filename = <span class="stringliteral">&quot;jump_result.m&quot;</span>;</div><div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;    file.open(filename.c_str());</div><div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;% Results file from &quot;</span> __FILE__ &lt;&lt; endl;</div><div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;% Generated &quot;</span> __DATE__ <span class="stringliteral">&quot; at &quot;</span> __TIME__ &lt;&lt; endl;</div><div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;    file &lt;&lt; endl;</div><div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;</div><div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;    <span class="comment">//file &lt;&lt; &quot;t = linspace(0,&quot; &lt;&lt; 0.31 &lt;&lt; &quot;,&quot; &lt;&lt; N &lt;&lt; &quot;);&quot; &lt;&lt; endl;</span></div><div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;xb= &quot;</span> &lt;&lt; std::vector&lt;double&gt;(sol.value(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(0, all) ) ) &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;zb= &quot;</span> &lt;&lt; std::vector&lt;double&gt;(sol.value(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(1, all))) &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;theta= &quot;</span> &lt;&lt; std::vector&lt;double&gt;(sol.value(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(2, all))) &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;dot_xb= &quot;</span> &lt;&lt; std::vector&lt;double&gt;(sol.value(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(3, all) ) ) &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;dot_zb= &quot;</span> &lt;&lt; std::vector&lt;double&gt;(sol.value(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(4, all))) &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;dot_theta= &quot;</span> &lt;&lt; std::vector&lt;double&gt;(sol.value(<a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>(5, all))) &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;</div><div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;Fx = &quot;</span> &lt;&lt; std::vector&lt;double&gt;(sol.value(F(0, all) ) ) &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;Fz = &quot;</span> &lt;&lt; std::vector&lt;double&gt;(sol.value(F(1, all) ) )&lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;</div><div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;    file &lt;&lt; <span class="stringliteral">&quot;P = &quot;</span> &lt;&lt; std::vector&lt;double&gt;(sol.value(P(all) ) ) &lt;&lt; <span class="stringliteral">&quot;;&quot;</span> &lt;&lt; endl;</div><div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;</div><div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;   <span class="comment">//file &lt;&lt; &quot;figure;&quot; &lt;&lt; endl;</span></div><div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;    <span class="comment">//file &lt;&lt; &quot;hold on;&quot; &lt;&lt; endl;</span></div><div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;    <span class="comment">//file &lt;&lt; &quot;plot(xb, zb);&quot; &lt;&lt; endl;</span></div><div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;</div><div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;    <span class="comment">//jacobian(opti.g(), opti.x()).sparsity().spy_matlab(&quot;jump_jac_g.m&quot;);</span></div><div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;</div><div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;    <span class="comment">//file &lt;&lt; &quot;figure&quot; &lt;&lt; std::endl;</span></div><div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;    <span class="comment">//file &lt;&lt; &quot;jump_jac_g;&quot; &lt;&lt; std::endl;</span></div><div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;    <span class="comment">//file &lt;&lt; &quot;xlabel(&#39;decision variables&#39;);&quot; &lt;&lt; std::endl;</span></div><div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;    <span class="comment">//file &lt;&lt; &quot;ylabel(&#39;constraints&#39;);&quot; &lt;&lt; std::endl;</span></div><div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;    <span class="comment">//file &lt;&lt; &quot;print(&#39;jac_sp&#39;,&#39;-dpng&#39;);&quot; &lt;&lt; std::endl;</span></div><div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;    file.close();</div><div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;  }</div><div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;}</div><div class="ttc" id="test__casadi_8cpp_html_a37cd3654eae85ab1ac98486587c52e22"><div class="ttname"><a href="../../dc/dd7/test__casadi_8cpp.html#a37cd3654eae85ab1ac98486587c52e22">simple_dyn</a></div><div class="ttdeci">MX simple_dyn(const MX &amp;x, const MX &amp;u, const MX &amp;P, int i)</div><div class="ttdef"><b>Definition:</b> <a href="../../dc/dd7/test__casadi_8cpp_source.html#l00297">test_casadi.cpp:297</a></div></div>
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<div class="ttc" id="test__casadi_8cpp_html_ae22a77a911d57b6e51df80a32a050b94"><div class="ttname"><a href="../../dc/dd7/test__casadi_8cpp.html#ae22a77a911d57b6e51df80a32a050b94">TEST</a></div><div class="ttdeci">TEST(casadi, rocket_ipopt)</div><div class="ttdef"><b>Definition:</b> <a href="../../dc/dd7/test__casadi_8cpp_source.html#l00019">test_casadi.cpp:19</a></div></div>
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<div class="ttc" id="_math_utilities_8h_html_aa06ec79f1e3170ea41b58ffbf35b9fb6"><div class="ttname"><a href="../../de/dda/_math_utilities_8h.html#aa06ec79f1e3170ea41b58ffbf35b9fb6">almostEqual</a></div><div class="ttdeci">bool almostEqual(const Eigen::MatrixBase&lt; T &gt; &amp;a, const Eigen::MatrixBase&lt; T &gt; &amp;b, T2 tol)</div><div class="ttdef"><b>Definition:</b> <a href="../../de/dda/_math_utilities_8h_source.html#l00023">MathUtilities.h:23</a></div></div>
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<div class="ttc" id="_dynamics_simulator_8h_html"><div class="ttname"><a href="../../d0/d52/_dynamics_simulator_8h.html">DynamicsSimulator.h</a></div><div class="ttdoc">Rigid Body Dynamics Simulator with Collisions. </div></div>
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<div class="ttc" id="test__casadi_8cpp_html_ae20d7fba59865a21504b65cdb44cbfe5"><div class="ttname"><a href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a></div><div class="ttdeci">MX f(const MX &amp;x, const MX &amp;u)</div><div class="ttdef"><b>Definition:</b> <a href="../../dc/dd7/test__casadi_8cpp_source.html#l00202">test_casadi.cpp:202</a></div></div>
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